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Adversarial examples, crafted by adding imperceptible perturbations tonatural inputs, can easily fool deep neural networks (DNNs). One of the mostsuccessful methods for training adversarially robust DNNs is solving anonconvex-nonconcave minimax problem with an adversarial training (AT)algorithm. However, among the many AT algorithms, only Dynamic AT (DAT) and YouOnly Propagate Once (YOPO) guarantee convergence to a stationary point. In thiswork, we generalize the stochastic primal-dual hybrid gradient algorithm todevelop semi-implicit hybrid gradient methods (SI-HGs) for finding stationarypoints of nonconvex-nonconcave minimax problems. SI-HGs have the convergencerate $O(1/K)$, which improves upon the rate $O(1/K^{1/2})$ of DAT and YOPO. Wedevise a practical variant of SI-HGs, and show that it outperforms other ATalgorithms in terms of convergence speed and robustness.

Semi-Implicit Hybrid Gradient Methods with Application to Adversarial Robustness